As a reference signal source in a several MHz frequency band used for an electronic device such as a portable device, an information communication device, and a measurement equipment, a contour resonator such as an AT cut quartz crystal resonator, a DT cut quartz crystal resonator (a contour shear mode quartz crystal resonator), a Lame mode quartz crystal resonator, and a quasi Lame mode quartz crystal resonator can be cited.
The Lame mode quarts crystal resonator is formed such that a plurality of small excitation electrodes having a square shape are arranged in the longitudinal and the lateral directions on both surfaces of a square shaped crystal substrate. In the resonator, electric fields having opposite polarities are applied to adjacent small excitation electrodes so as to generate contour vibrations around boundary of a small vibrating part with reference to vibration nodes at four corners of each of the small excitation electrodes (Refer to Patent Citation 1, for example).
If an area for forming the small excitation electrodes is 50% or more of whole area of the small vibrating part in the Lame mode quartz crystal resonator, an equivalent resistance value has no problem practically. If the area is 70% or more, an enormous reduction effect of the equivalent resistance value can be expected. However, since a gap for forming an insulating pattern and a wiring pattern has to be ensured between the small vibration electrodes, the area is preferably 80% to 90%.
Further, a piezoelectric resonator in which excitation electrodes are provided on both front and back surfaces of a piezoelectric mother substrate vibrates in an area mode (Refer to Patent Citation 2, for example). The piezoelectric mother substrate is made of PZT®, quartz crystal, LaTaO3, and the like. The excitation electrodes are made of Ag, Pd, Ni, Cu, Au, or those alloys.
Non Patent Citation 1 discloses a Lame mode quartz crystal resonator expressed by (YX1t)phi/theta of IRE (abbreviation of Institute of Radio Engineers, that is, current IEEE) standard shown in FIG. 10. In terms of the resonator, a resonance frequency (contour vibration frequency) f of a quartz substrate is derived by a frequency equation shown in Math (9) of the citation. In addition, a resonance frequency of the excitation electrode can be derived from the frequency equation. Non Patent Citation 2 also mentions this.    Patent Citation 1: JP-A-2002-111434 (page 4, FIG. 1)    Patent Citation 2: JP-A-8-97667 (page 2-3, FIG. 8)    Non Patent Citation 1: “Lame-mode quartz-crystal resonator formed by an etching method” by Hirofumi Kawashima, and Masaru Matsuyama in the 24th EM symposium, page 11 to 16, Math (2), conditional clause and Math (9)    Non Patent Citation 2: “Development of a small-sized Lame-mode quartz-crystal resonator” by Katsuya Mizumoto, Masashi Akino, Tsuyoshi Nishizuka, Hideki Ashizawa, Masahide Marumo, and Masato Amemiya in the 35th EM symposium, page 31 to 34